Experimental and numerical investigations reveal that nonlinear modulational instability can significantly affect the probability of occurrence of extreme waves, especially if waves are sufficiently steep and narrow banded both in the frequency and directional domain. However, it is not yet completely clear whether numerical simulations can provide an accurate quantitative estimate of experimental results. Here the potential Euler equations are used to assess the ability of numerical models to describe the evolution of statistical properties of mechanically generated directional, random wave fields and in particular the evolution of the kurtosis. Results show that simulations provide a good quantitative estimate of experimental observations within a broad range of wave directional width.